HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 183
MODULO menu, Applications of the ARITHMETIC menu, Modular arithmetic
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MODULO menu ADDTMOD Add two expressions modulo current modulus DIVMOD Divides 2 polynomials modulo current modulus DIV2MOD Euclidean division of 2 polynomials with modular coefficients EXPANDMOD Expands/simplify polynomial modulo current modulus FACTORMOD Factorize a polynomial modulo current modulus GCDMOD GCD of 2 polynomials modulo current modulus INVMOD inverse of integer modulo current modulus MOD (not entry available in the help facility) MODSTO Changes modulo setting to specified value MULTMOD Multiplication of two polynomials modulo current modulus POWMOD Raises polynomial to a power modulo current modulus SUBTMOD Subtraction of 2 polynomials modulo current modulus Applications of the ARITHMETIC menu This section is intended to present some of the background necessary for application of the ARITHMETIC menu functions. Definitions are presented next regarding the subjects of polynomials, polynomial fractions and modular arithmetic. The examples presented below are presented independently of the calculator setting (ALG or RPN) Modular arithmetic Consider a counting system of integer numbers that periodically cycles back on itself and starts again, such as the hours in a clock. Such counting system is called a ring. Because the number of integers used in a ring is finite, the arithmetic in this ring is called finite arithmetic. Let our system of finite integer numbers consists of the numbers 0, 1, 2, 3, ..., n-1, n. We can also refer to the arithmetic of this counting system as modular arithmetic of modulus n. In the case of the hours of a clock, the modulus is 12. (If working with modular arithmetic using the hours in a clock, however, we would have to use the integer numbers 0, 1, 2, 3, ..., 10, 11, rather than 1, 2, 3,...,11, 12). Page 5-12
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